rp = a(1 − e) and ra = a(1 + e), respectively.

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1. Show that the closest and farthest approach (called the pericentre and apocentre, respectively) of a star
on a Kepler orbit are given by rp = a(1 − e) and ra = a(1 + e), respectively.

a)Calculate rp and ra in terms of the specific energy E, specific angular momentum J, G and M.

b)By matching rp = a(1 − e) and ra = a(1 + e) to your derivation above, write down the semi-major axis a
and eccentricity e in terms of E, J, M and G.

kindly help me solve it. Its urgent.

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